Project 2 evaluates advanced methods for analyzing patterns in epidemiologic and toxicologic data involving combinations of space and time or combinations of chemicals (mixtures). Two SRP mandates are addressed: (1) advanced technicues to detect associations between human health effects and environmental hazards; (2) methods to assess the risks to human health presented by hazardous substances. There are four related research aims and one research translation aim. Aim 1 is a rigorous evaluation of the use of tensor product smooths in generalized additive models (GAMs) to analyze spacetime interactions in epidemiological data. GAMs predict local disease odds over time while adjusting for known risk factors in the population. Aim 2 will apply GAM methods to investigate patterns in space and time for two populations: birth defects in parts of Massachusetts and Rhode Island (formal collaboration with SRP Project 1), and Attention Deficit Hyperactivity Disorder (ADHD)-related behaviors in children born while their mothers were living near the New Bedford Harbor Superfund Site. Aim 3 extends the application of our spatial methods to the analysis of chemical mixtures (formal collaboration with SRP Projects 4 and 6). In Aim 4, we assess combinations of exposures in epidemiology, adapting methods from toxicology. Aim 5 will make the methods developed in our project freely available via open source software, in collaboration with the Research Translation Core. The novel methods from this project should be of interest to academia, government and community organizations.